Valid Parentheses by Deleting One Character

You are given a string s consisting of lowercase English letters and parentheses (' and ')'. Your task is to determine whether it is possible to obtain a valid string by deleting at most one character from s.

A string is considered valid if the parentheses in the string are balanced. In other words, every opening parenthesis ( must have a corresponding closing parenthesis ) in the correct order.

The validation can be mathematically described by the following condition: if we process the string from left to right while increasing a counter for every ( and decreasing it for every ), then the counter should never be negative and must be zero after processing the entire string. This can be represented in LaTeX as:

$$\forall i,\; count_i \ge 0 \quad \text{and} \quad count_{\text{end}} = 0.$$

If the original string is already valid, the answer is YES. Otherwise, check if removing exactly one character makes it valid. If so, print YES; otherwise, print NO.

inputFormat

The input consists of a single line containing the string s.

Note: The string may contain lowercase letters and the characters '(' and ')'.

outputFormat

Output a single line: YES if it is possible to obtain a valid string by deleting at most one character; otherwise, output NO.

## sample

a(b)c)

YES

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